|Sep22-10, 03:21 PM||#137|
The Space Hose
Breaking under its own weight is a different story entirely. However, if you use nylon, this problem gets a lot simpler.
What you described is different than a circular flag, there are many reasons why it is different than a circular flag. The most prominent of which is the fact that a "flag" is generally horizontal, and a "tube" is generally vertical. The second most prominent of which is the fact that when you extend this tube such a distance, the frictional losses prevent air from reaching the other end without manual pumping. This pumping changes the problem from that of friction to that of pressure/structural rigidity.
|Sep22-10, 03:54 PM||#138|
A flag is also fighting gravity - hence the wording is not that bad :-)
Even Dyneema which is already pretty strong at a reasonable price/strenght ratio is able to hold already 300-400km of its own weight. But if you attach it to a hose which is able to hold the weight you can even avoid this problem to some extent.
If you would have a rocket with enough fuel to stay stationary in 100km height above ground you could already now hang a Dyneema string down and let climb everything which the rocket is able to hold as extra weight.
And there are rockets pulling cables - ask the US army - they call this an anti tank weapon and use the wire for steering it. But this concept runs out of usability beyond a (few) km or something.
Actually the picture of the Space Elevator climber challenge with the helicopter holding a 1km steel cable was also a big inspiration for me.
Regarding the friction force. The formular I used is designed for a horizontal PIPE. And the pressure loss it reports is only 0,6bar over 100km. Well, the problem ist that the formular is not designed for this, but theoretically if you would blow into such a pipe with 0,6 bar at this relatively low speed (3,5m/sec is a soft breeze if you do some sailing) the whole pressure should be eaten up on the end and you would blow out at 1 bar (which you would do when the end is open in any case).
If you now would use a hose instead of a pipe nothing really changes, if the hose is blown trough at the ground, except that you suddenly blow out in almost vaccum (100Pa) and instead of transferring all the friction force to the ground where the pipe was laying it will pull the hose upwards - against its own weight. I just tried to find what would be needed to reach an equilibrium of these 2 forces.
if you put the pipe/hose upright you simply have to add hydrostatic pressure (at least Mr. Bernoulli saiys so), Which for air is not a real problem, because the air outside does the same and hence the pressure should be always balanced. But I'm not even sure in what way this friction force would be transferred to the hose - blowing with extra speed (almost 300m/s as the slide suggest), or with the 0,6bar surpressure (bad but a Dyneema wrapped hose could still hold this) plus the suggested 3,5m/s ? But it is an open hose not a pipe, so normally there should be no surpressure except from the diffusor ?
BUT what is even more strange is that when you move 1m³ from bottom to top it will dramatically expand (would be 1000x in case temperature would be the same, but temperature on ground is 20 degree and in 100km it is -90 degree of celsius, hence expansion is only 625x). Friction is dependent on dynamic viscosity (dependant on temperature and density of the gas) and on the speed of flow². So friction in general is likely to go up because v² should win. Which would mean the upper part of the hose should eben get more friction and pull (unless you change the diameter). And the friction is even worser, if pressure drop occures due to it, it should create additional speed increase (Bernoulli - remember). But if you get so much speed from expansion already you don't need to feed it all at the ground in my understanding, and there should be an equlibrium of blowing an friction.
But it is even more confusing, after 100x expansion at about 50km height (there you have approximately 1000Pa pressure outside) the flow would reach the speed of sound without friction. And after this if you reduce the pressure further (which the atmosphere does for you) the speed would go further up, and because of the sonic border the hose would not even know that it is open or not. This is scaring, I intentionaly wrote in the slides the crazy question about a fixed diamter de Laval Nozzle :-)
On the other hand if friction really works and the speed stays in a sensemaking range, worst case would be that the friction converts to heat, which means further expansion and chimney effect in the hose giving also upwards flow.
Do you understand now that it is NOT that easy to say after a few kilometer it doesn't matter if the hose is open or upright, it will be like blowing into a kind of huge tank which at the end is only a crazy way of heating the whole device ?
So the real probably will be somewhere in between - air flow and supressure and expansion and friction, and ...
Because expansion and continuity law are still on our side, and as long there is flow you have friction - which always creates a force on the wall/hose which should be able to keep its weight if properly desinged ?
And remeber the whole thing is 100km long, so ALL speed and pressure gradients are extremely moderate (that's why I suggested a finite element calculation with 100m pieces in a spreadsheat to get some more accurate results on the speed and pressure gradient), this is not really the typical supersonic wind tunnel with extreme forces. I just decided some basic parameters like diameter and thickness and did some math - if we would have a proper model of the flow inside you would need to iterate it for finding the optimal parameters which could also include diameter changes to control the velocity - but then you would be in trouble when erecting the hose, etc.
Actually the whole thing is much more complex then it looks at first glance so saying yes or no is not that easy then I thought.
Which brings me back to my confusion and the reason why I have put it on slides and asked open and honestly for help !
|Sep25-10, 03:59 AM||#139|
Just a small update so that you don't think I have forgotten you or got completely lost:
I have spent the last few days to build a spreadsheet which calculates the standard atmosphere from 0 to 100km in 1km pieces, and then applied the formulars of the slides to these pieces to better understand what happens in the hose.
Then yesterday (during my morning shower!) I actually found out why I had so big problems getting sensemaking results:
It was a typical border value problem. Actually I always tried to calculate from bottom to top, but it is much easier to do it top to bottom, because there you simply define the maximum blowout speed (for example speed of sound to prevent the hose going supersonic) and the needed surpressure required to hold the payload and provide sufficient pull power to keep the hose stable.
Then you calculate the pressure loss of the resulting flow 1km down, add it to the atmospheric pressure there and the requested surpressure and get with ideal gas law a new density there, and hence a new flow speed because of continuity law. This means a new Reynolds number and a new viscosity and Lambda which means you have all the starting values for the next 1km and so on.
The pressure and blowing speed at the bottom are then a simple result of this iteration down and not the other way around. Because you can change pressure and blowing speed at the bottom in a relatively wide range depending what pump/fan you use this is not really a problem, and much better then choosing them and then get weird results at the top and within the hose.
Then you calculate the speed of sound at all these points to check that nowhere the air flow is faster. When you then have the flow and pressure gradient of the entire hose you can calculate the tension forces in the hose and can check if the PE foil and/or Dyneema strength can hold it.
If you blow out at the speed of sound this also becomes a kind of event horizon, meaning the hose doesn't care/know what the diffusor afterwards does, if you add a de Laval nozzle to blow out supersonic, turn the air flow downwards to generate lift, etc.
Then you are done and have a Spreadsheet where you can start playing with different blowout speeds, diffusor pressures, different foil thickness, hose diameters,... to find the optimal hose.
I will polish the spreadsheet a little bit more so that everybody can use it and then probably tomorrow you can play with it. There are some quite interesting findings already from what I tried out.
So actually the formulars and the math was not that bad (and there was no real critics from you on this either), but the USAGE was simple a little bit dumb and I should have tried it the way I suggested already earlier instead of trying to enter 100km in a single formular which allows to get an idea if it would work, but produces only consfusion on how.
Thanks for your patience with me!
|Sep25-10, 09:24 AM||#140|
Cool. I'd be interested in your first take on fan speed/pressure.
|Sep25-10, 10:58 AM||#141|
Funny is that the top contributes most of the pull forces even without the diffusor, which is good for extra stability. I already assumed this (because of the v² of the friction forces, but I didn't have any idea to what extent)
I'll see if I can warp it up and add some comments and colors for the changabel fields until this evening than you can play with it yourself.
Having such a 'virtual Space Hose' where all the parameters are changeable is pretty funny, and it even gives interesting results like pressure waves on top if the surpressure is too low, or how low you can bring the hose tensions down before it fails to stay errect (approximately 100N/mm² - which is not so far away from plain PE)
As I already mentioned I'm doing also some open source software development as another hobby so as soon as I found the formulars on how to calculate the Standard Atmosphere model from the definitions it was not so diffucult to build a Spreadsheet out of it.
Then I found another Webpage where you can calculate air viscosity for all temperatures:
It took me almost 1 hour to get all 100 viscosities for the model, but I was too lazy to try to reverse engineer the math for this too :-)
From these two raw inputs you have everything needed for the pressure loss calculation at all heights, and then the fun started when putting it together.
|Sep25-10, 11:35 AM||#142|
One more question on the wind - I found a nice picture on this (see attachment)
Would this mean that a hose with pull from top would actually form more or less such a bent curve ?
Because I would like to include also the pull force calculation into the excel, and for this I need a better understanding of the distribution of the wind force on the lower end of the hose.
|Sep26-10, 11:24 AM||#143|
Damned - I still have problems with my Excel and the discrete calculation steps because now I have a circular reference.
If I go 1km down this means that the pressure on the bottom should be the one at the top + pressure loss from friction + hydrostatic pressure of the 1km of gas.
The problem is that hydrostatic pressure is dependant on the density, which is resulting from the pressure from bottom to top (if I asume that temperature is always aproximately outside temperature of the standard atmosphere) = circular reference. Now I understand why the books are saying this is a differetial equation with an integral which is only numericially solveable - if at all :-(
And if I try to overcome this by simply taking the previous density as I did until now the result is underestimating pressure, which makes the numbers look good, but then the model is invalid beyond the top few kilometers of the hose, because only there density and hence hydrostatic pressure is low enough to allow such a simplification. So calculating top to bottom was a good idea, but gives wrong results at the bottom because of the discretisation. This is also the reason why going from bottom to top produced too high numbers on top.
But problems are there to be solved, and input is welcome ;-)
|Nov4-10, 04:13 PM||#144|
Is the "space hose" thread over?
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